Abstract

The stability of an infinite-length cylindrical shell subjected to a broad class of axially symmetric moving loads with constant velocity is studied by utilizing a large deflection Donnell theory. Special cases of the general loading function include the moving ring, step and decayed step loads.

Stability is defined on the basis of the boundedness or divergence of an infinitesimal nonsymmetric disturbed motion about an initial nonlinear steady-state symmetric response. Following the determination of the symmetric response, under this concept of stability, the analysis is reduced to a study of a system of linear partial differential equations or so-called variational equations; these are analyzed by use of a double Laplace transform technique and the original stability problem is replaced by a simpler one of determining the location of the poles of a certain function. A scheme for accomplishing this task is outlined. Extension of the method to include more exact equations of motion and to a class of static problems involving finite length shells is discussed.

A related problem concerning a moving concentrated load on a nonlinear elastic cylindrical membrane (nonlinearity in both geometric and constitutive relations) and a string on a nonlinear foundation is discussed in an appendix to the text. Interesting analogies in both analysis and physical behavior of the string and shell systems are found.